A centrifugal draining pump of that type is described in a U.S. patent application Ser. No. 10/723,295 which published as publication number US2005/0111992. Pumps of the type generally disclosed in this publication were designed to solve the problem of the motor being easily burned out owing to heavy load during initial start-up of the pump. The major contribution of the invention is to improve the start-up coupling between a shaft sleeve and an impeller. As shown in the figures of the publication referred to above, a coupling formation of the rotor is set up on the drive body, and a coupling formation of the impeller is set up inside of the impeller. A pair of end portions that is constructed of resilient materials with intermediate connecting and retaining portions are molded onto two opposite surfaces of an appendage of the coupling formation of the drive body so as to reduce noise and absorb shock. However, such a configuration is quite complicated and suffers from higher costs of manufacture and maintenance.